Abstract
We characterize (non)Markovian dynamics of open quantum systems. Two recently proposed measures of non-Markovianity are analyzed: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. The characterization of the correspondingg enerators in the Heisenberg picture is provided as well.
Mathematics Subject Classification (2010). Primary 47L05; Secondary 81Q05.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford Univ. Press, Oxford, 2007).
U. Weiss, Quantum Dissipative Systems, (World Scientific, Singapore, 2000).
R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications (Springer, Berlin, 1987).
M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).
V. Gorini, A. Kossakowski, and E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976). Characterizing Non-Markovian Dynamics 293
G. Lindblad, Comm. Math. Phys. 48, 119 (1976).
C.W. Gardiner and P. Zoller, Quantum Noice, Springer-Verlag, Berlin, 1999.
A. Kossakowski and R. Rebolledo, Open Syst. Inf. Dyn. 14, 265 (2007); ibid. 16, 259 (2009).
H.-P. Breuer and B. Vacchini, Phys. Rev. Lett. 101 (2008) 140402; Phys. Rev. E 79, 041147 (2009).
E.-M. Laine, J. Piilo, and H.-P. Breuer, Phys. Rev. A 81, 062115 (2010).
L. Mazzola, E.-M. Laine, H.-P. Breuer, S. Maniscalco, and J. Piilo, Phys. Rev. A 81, 062120 (2010).
T.J.G. Apollaro, C. Di Franco, F. Plastina, and M. Paternostro, Phys. Rev. A 83, 032103 (2011).
D. Chruściński and A. Kossakowski, Phys. Rev. Lett. 104, 070406 (2010).
D. Chruściński, A. Kossakowski, and S. Pascazio, Phys. Rev. A 81, 032101 (2010).
M.M. Wolf and J.I. Cirac, Comm. Math. Phys. 279, 147 (2008); M.M. Wolf, J. Eisert, T.S. Cubitt and J.I. Cirac, Phys. Rev. Lett. 101, 150402 (2008).
H.-P. Breuer, E.-M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
Á. Rivas, S.F. Huelga, and M.B. Plenio, Phys. Rev. Lett. 105, 050403 (2010).
P. Haikka, J.D. Cresser, and S. Maniscalco, Phys. Rev. A 83, 012112 (2011)
D. Chruściński, Kossakowski and Á. Rivas, Phys. Rev. A 83, 052128 (2011).
V. Paulsen, Completely Bounded Maps and Operator Algebras, Cambridge University Press, 2003.
R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
S.L. Woronowicz, Rep. Math. Phys. 10, 165 (1976).
D. Chruściński and A. Kossakowski, J. Phys. A: Math. Theor. 41, (2008), 145301; J. Phys. A: Math. Theor. 41, 215201 (2008); Phys. Lett. A 373 2301 (2009).
D. Chruściński and A. Kossakowski, Comm. Math. Phys. 290, 1051 (2009).
D. Chruściński and J. Pytel, J. Phys. A: Math. Theor. 44, 165304 (2011).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated to honor Professor Woronowicz on the occasion of his 70th birthday.
Rights and permissions
Copyright information
© 2013 Springer Basel
About this paper
Cite this paper
Chruściński, D., Kossakowski, A. (2013). Characterizing Non-Markovian Dynamics. In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_23
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0448-6_23
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0447-9
Online ISBN: 978-3-0348-0448-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)